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# help pls

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A unit square is drawn. Then an equilateral triangle is constructed on each side of the unit square, and the four new points of the diagram are joined to form a larger square. Find the area of the larger square. Dec 26, 2019

#1
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Combining the areas of all the regions, I'm getting that the area of the large square is 3 + 2*sqrt(3).

Dec 26, 2019
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The height, H,  of one of the equilateral triangles   can be found as

tan 60   =   H /(1/2)

√3/2  = H

The diagonal of the square  =   2H  + 1 =   √3  +  1

The side of the larger  square = diagonal / √2  =     [ √3 + 1  ]  / √2

So....the area  of the larger square  =

[ √3 + 1 ] ^2 / 2     =    [ 3 + 2√3 + 1' / 2   =  [4 + 2√3 ] / 2   =   [ 2 + √3 ]  units^2  ≈  3.732 units^2   Dec 26, 2019
#4
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Smaller square side                  a = 1

Equilateral triangle side             s = 1

Equilateral triangle height         h =  sqrt [ s2 - ( s/2)2 ]       h = sqrt [ 1 - (1/2)2 ]  = 0.866

The area of a larger square      A = 2( h + a/2 )2                 A = 2(0.866+0.5)2  =  3.732 u2 Dec 26, 2019
#5
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Good job, Dragan   !!!!   CPhill  Dec 26, 2019
#8
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u r w

Dragan  Dec 26, 2019